scholarly journals Exploiting Spatial Information to Enhance DTI Segmentations via Spatial Fuzzy c-Means with Covariance Matrix Data and Non-Euclidean Metrics

2021 ◽  
Vol 11 (15) ◽  
pp. 7003
Author(s):  
Safa Elsheikh ◽  
Andrew Fish ◽  
Diwei Zhou
Keyword(s):  
Spatial Information ◽  
Diffusion Tensor ◽  
Contextual Information ◽  
Fuzzy C Means ◽  
Tensor Models ◽  
Diffusion Tensor Images ◽  
Fuzzy C Means Clustering ◽  
Euclidean Metrics ◽  
Diffusion Tensors ◽  
Tensor Data

A diffusion tensor models the covariance of the Brownian motion of water at a voxel and is required to be symmetric and positive semi-definite. Therefore, image processing approaches, designed for linear entities, are not effective for diffusion tensor data manipulation, and the existence of artefacts in diffusion tensor imaging acquisition makes diffusion tensor data segmentation even more challenging. In this study, we develop a spatial fuzzy c-means clustering method for diffusion tensor data that effectively segments diffusion tensor images by accounting for the noise, partial voluming, magnetic field inhomogeneity, and other imaging artefacts. To retain the symmetry and positive semi-definiteness of diffusion tensors, the log and root Euclidean metrics are used to estimate the mean diffusion tensor for each cluster. The method exploits spatial contextual information and provides uncertainty information in segmentation decisions by calculating the membership values for assigning a diffusion tensor at one voxel to different clusters. A regularisation model that allows the user to integrate their prior knowledge into the segmentation scheme or to highlight and segment local structures is also proposed. Experiments on simulated images and real brain datasets from healthy and Spinocerebellar ataxia 2 subjects showed that the new method was more effective than conventional segmentation methods.

scholarly journals On What Manifold do Diffusion Tensors Live?

2008 ◽  
Author(s):  
Ofer Pasternak ◽  
Ragini Verma ◽  
Nir Sochen ◽  
Peter J. Basser
Keyword(s):  
Diffusion Tensor ◽  
Affine Invariant ◽  
Clinical Tool ◽  
Basic Notion ◽  
Euclidean Metric ◽  
Statistical Framework ◽  
Euclidean Metrics ◽  
Diffusion Tensors ◽  
Tensor Data ◽  
Confidence Estimates

Diffusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diffusion tensor data and perform, for example, confidence estimates, ROI analysis, and group comparisons. A first step towards developing a statistical framework is establishing the basic notion of distance between tensors. We investigate the properties of two previously proposed metrics that define a Riemannian manifold: the affine-invariant and Euclidean metrics. We find that the Euclidean metric is more appropriate for intra-voxel comparisons, and suggest that a context-dependent metric may be required for inter-voxel comparisons.

scholarly journals Denoising of brain DW-MR data by single and multiple diffusion kernels

2010 ◽  
Vol 20 (3) ◽  
pp. 44-50
Author(s):  
Alonso Ramírez-Manzanares ◽  
Jonathan Rafael-Patiño ◽  
Manzar Ashtari
Keyword(s):  
Spatial Information ◽  
Diffusion Tensor ◽  
Signal To Noise Ratio ◽  
Tensor Models ◽  
Different Types ◽  
Weighted Magnetic Resonance Imaging ◽  
Axon Bundle ◽  
The Brain ◽  
Spatial Regularization

Diffusion Weighted Magnetic Resonance Imaging is widely used to study the structure ofthe fiber pathways of white matter in the brain. However, the recovered axon orientationscan be prone to error because of the low signal to noise ratio. Spatial regularization canreduce the error, but it must be done carefully so that real spatial information is not removedand false orientations are not introduced. In this paper we investigate the advantagesof applying an anisotropic filter based on single and multiple axon bundle orientation kernels.To this end, we compute local diffusion kernels based on Diffusion Tensor and multiDiffusion Tensor models. We show the benefits of our approach to three different types ofDW-MRI data: synthetic, in vivo human, and acquired from a diffusion phantom.

Adaptive Kernel-Based Fuzzy C-Means Clustering with Spatial Constraints for Image Segmentation

2018 ◽  
Vol 33 (01) ◽  
pp. 1954003 ◽  
Author(s):  
Guang Hu ◽  
Zhenbin Du
Keyword(s):  
Image Segmentation ◽  
Clustering Algorithm ◽  
Spatial Information ◽  
Spatial Constraints ◽  
Fuzzy C Means ◽  
Central Pixel ◽  
Fuzzy C Means Clustering ◽  
Adaptive Kernel ◽  
Fcm Clustering ◽  
Image Pixels

In order to resolve the disadvantages of fuzzy C-means (FCM) clustering algorithm for image segmentation, an improved Kernel-based fuzzy C-means (KFCM) clustering algorithm is proposed. First, the reason why the kernel function is introduced is researched on the basis of the classical KFCM clustering. Then, using spatial neighborhood constraint property of image pixels, an adaptive weighted coefficient is introduced into KFCM to control the influence of the neighborhood pixels to the central pixel automatically. At last, a judging rule for partition fuzzy clustering numbers is proposed that can decide the best clustering partition numbers and provide an optimization foundation for clustering algorithm. An adaptive kernel-based fuzzy C-means clustering with spatial constraints (AKFCMS) model for image segmentation approach is proposed in order to improve the efficiency of image segmentation. Various experiment results show that the proposed approach can get the spatial information features of an image accurately and is robust to realize image segmentation.

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